Question: Solve for $x$ and $y$ using substitution. ${-5x-3y = 7}$ ${y = -x+1}$
Answer: Since $y$ has already been solved for, substitute $-x+1$ for $y$ in the first equation. ${-5x - 3}{(-x+1)}{= 7}$ Simplify and solve for $x$ $-5x+3x - 3 = 7$ $-2x-3 = 7$ $-2x-3{+3} = 7{+3}$ $-2x = 10$ $\dfrac{-2x}{{-2}} = \dfrac{10}{{-2}}$ ${x = -5}$ Now that you know ${x = -5}$ , plug it back into $\thinspace {y = -x+1}\thinspace$ to find $y$ ${y = -}{(-5)}{ + 1}$ $y = 5 + 1$ $y = 6$ You can also plug ${x = -5}$ into $\thinspace {-5x-3y = 7}\thinspace$ and get the same answer for $y$ : ${-5}{(-5)}{ - 3y = 7}$ ${y = 6}$